Question 22Let $M$ be the set of mappings $\phi:\{1,2,3,4\}\to\{c_1,c_2,c_3\}$ such that $\phi(1)\ne\phi(2)$, $\phi(2)\ne\phi(3)$, $\phi(3)\ne\phi(4)$ and $\phi(4)\ne\phi(1)$. Determine the number of mappings in $M$.